We can also adapt the boundedness-from-below necessary conditions from Ref. [1]} (see Eqs. (21)–(24) there), being careful with the fact that the potential of that work is different from the one considered here (our potential has a more restrictive symmetry, and therefore has fewer quartic couplings). This translates into a generalisation of the above conditions, which become
\(\lambda _4\,>-\,2\sqrt{\lambda _1 \lambda _2}\,-\,{\rm min}(0,\lambda _7) \;\; , \;\;\lambda _5\,>-\,2\sqrt{\lambda _1 \lambda _3} \,-\,{\rm min}(0,\lambda _8 - 2|\lambda _{10}|)\;\; , \;\;\lambda _6\,>-\,2\sqrt{\lambda _2 \lambda _3} \,-\,{\rm min}(0,\lambda _9) \,.\) 
